Average of Levels in Binary Tree

Average of Levels in Binary Tree - Problem

Given the root of a binary tree, return the average value of the nodes on each level in the form of an array.

Answers within 10^-5 of the actual answer will be accepted.

Input & Output

Example 1 — Basic Tree

$ Input: root = [3,9,20,null,null,15,7]

› Output: [3.0,14.5,11.0]

💡 Note: Level 0: node 3 → average = 3.0. Level 1: nodes 9,20 → average = (9+20)/2 = 14.5. Level 2: nodes 15,7 → average = (15+7)/2 = 11.0

Example 2 — Single Node

$ Input: root = [1]

› Output: [1.0]

💡 Note: Only one level with single node 1, so average is 1.0

Example 3 — Left-Heavy Tree

$ Input: root = [3,9,20,15,7]

› Output: [3.0,14.5,11.0]

💡 Note: Level 0: node 3 → 3.0. Level 1: nodes 9,20 → 14.5. Level 2: nodes 15,7 → 11.0

Constraints

The number of nodes in the tree is in the range [1, 10⁴]
-2³¹ ≤ Node.val ≤ 2³¹ - 1

Visualization

Tap to expand

Asked in

A Amazon 35 F Facebook 22 L LinkedIn 18 M Microsoft 15

The key insight is to process the tree level by level using BFS (breadth-first search). For each level, calculate the sum of all node values and divide by the count to get the average. Best approach is BFS with queue for O(1) space per level. Time: O(n), Space: O(w) where w is maximum tree width.

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

DFS with Level Tracking

⏱️ Time: O(n) Space: O(n)

Traverse the tree using DFS while keeping track of the current level. Store all node values for each level in separate lists, then compute the average for each level at the end.

Level-Order BFS

⏱️ Time: O(n) Space: O(w)

Process the tree level by level using a queue. For each level, calculate the sum and count of nodes, then compute the average directly without storing all values.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

185.0K Views

Medium Frequency

~15 min Avg. Time

2.9K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen